We consider space-times with two isometries which represent gravitational waves with distinct wavefronts which propagate into exact Friedmann Robertson Walker (FRW) universes. The geometry of possible wavefronts is analysed in detail in all three types of FRW models. In the spatially flat and open universes, the wavefronts can be planar or cylindrical; in the closed case they are toroidal. Exact solutions are given which describe gravitational waves propagating into the FRW universes with a fluid with a stiff equation of state. It is shown that the plane-fronted waves may include impulsive or step (shock) components, while the cylindrical waves in the spatially flat and open universes and the toroidal waves in closed universes may contain steps. In general, wavefronts may exist which have an arbitrary finite degree of smoothness. In all cases, the waves are backscattered. The head-on collision of such waves is also briefly mentioned.
1996 Academic Press, Inc.
1. Introduction
Most work on gravitational waves in cosmological backgrounds has been based on first order approximation methods. However, if gravitational radiation played a significant role in the universe, then the waves would cause the symmetries of the standard homogeneous and isotropic models to be violated. In order to treat general, large perturbations one has to turn to a numerical approach. However, when space-time is assumed to have two spacelike Killing vectors, exact solutions containing gravitational waves or solitons can be constructed, at least for vacuum or for scalar or electromagnetic fields or for a stiff perfect fluid in which the pressure article no. 0128 180 0003-4916Â96 18.00